In Wu and Emanuel (1993, 1994), the results of the advection flow of Bob show that Bob's movement is due not only to the climatological (July-September) mean balanced flow, but also to significant contributions from the balanced flow associated with the upper-tropospheric PV perturbations (U) [Fig. 4(a)]. This implies that Bob's motion is strongly influenced by the mid-latitude systems and the disturbances in the upper troposphere. However, in the case of Ana, the advection of this tropical storm is mainly associated with the mean flow and the PV perturbation in the lower troposphere. Unlike the case of Bob, due to the cancellation effects between the PV anomalies (i.e. the balanced flows associated with different pieces of the upper PV anomalies tend to aim toward different directions), the upper PV perturbation does not have a large effect on Ana's motion [Fig. 4(b)]. And for Hurricane Andrew, the climatological mean, upper and lower PV perturbations have about the same magnitude of contribution to the advection flow [Fig. 4(c)].

Compared to the annular mean winds, the analysis by Wu and Emanuel (1995a,b) provides a more dynamically consistent method of determining the advection flow through the hurricane center. In addition, the PV framework is conceptually more concise (Hoskins et al., 1985), and allows one to study the essential dynamical mechanism responsible for hurricane motion.

(2) A new look at the binary interaction: potential vorticity diagnosis of the unusual southward motion of Tropical Storm Bopha (2000) and its interaction with Supertyphoon Saomai (2000) (Wu et al., 2003) Tropical Storm Bopha (2000) showed a very unusual southward course parallel to the east coast of Taiwan, mainly steered by the circulation associated with Supertyphoon Saomai (2000) to Bopha's east.

To quantitatively measure the influence of the steering flow associated with other PV features in this binary interaction, the method shown in Subsec. 3.2(2) is adopted. Results show that the total PV perturbation provides

a good approximation of the actual motion of both storms, Bopha and Saomai. Besides, Saomai plays the dominant role in advecting Bopha southward while the influence of Bopha on Saomai is rather limited (Fig. 5).

To better indicate the binary interaction processes, the new method for ploting the centroid-relatice track is devised. As shown in Fig. 6, Bopha and Saomai mutually interacted by rotating cyclonically around each other at a distance of about 1200 km, with the centroid much closer to Saomai. The unusual southward drift of Bopha appears to agree with the proposed mechanism as the direct binary interaction with one-way influence (Carr et al., 1997). Clearly, the above PV analysis with the AT values can nicely quantify the binary interaction processes, and the newly defined centroid-relative track can describe the appropriate interaction of the TCs.

Typhoons over the western North Pacific often move westward or northwestward due to the dominating steering flow associated with the Pacific Subtropical High (SH). However, forecasts of typhoons are sometimes difficult during the late season as typhoons approach about 130° E, where some storms may slow down, stall, or even recurve due to the weakening of the SH, as well as the strengthening of the Continental High (CH) over China and the presence of the deep midlatitude baroclinic wave or trough (TR). The stalling scenario appeared in the case of Sinlaku, where forecasts from some major operational centers failed to predict its slowdown and mistakenly predicted its southward dip before it approached the offshore northeastern Taiwan.

The PV diagnosis indicates that the initial deceleration of Sinlaku was mainly associated with the retreat of the SH under the influence of the TR. The upper-level cold-core low (CCL) played only a minor role in impeding Sinlaku from moving northward, while the CH over mainland China strongly steered Sinlaku westward. On account of the steering effects from the above four systems (SH, TR, CCL, and CH), which tend to cancel one another, the subtle interaction therein makes it difficult to make a precise track forecast (Fig. 7). This proposes another challenge to TC track forecasts in this region.

3.4. Summary

The validity of balance dynamics in the tropics allows us to explore the dynamics of hurricanes using the PV framework. Subsection 3.3 demonstrated the use of PV diagnostics in understanding the hurricane steering flow, and the interaction between the cyclone and its environment. The results are consistent with the previous finding that the hurricane advection flow, defined by inverting the entire PV distribution which excludes the storm's own positive anomaly, is a good approximation to real cyclone movement, even though the original data cannot capture the actual hurricane strength.

Moreover, the binary interaction between two typhoons is well demonstrated by the PV diagnosis. The quantitative description of the Fujiwhara effect is not easy for real-case TCs, because it tends to be masked by other environmental steering flows. A new centroid-relative track is proposed, with the position weighting based on the induced steering flow due to the PV anomaly of another storm. Such analysis is used to understand more complicated vortex merging and interacting processes between and among multiple TCs from either observational data or specifically designed numerical experiments. Finally, the PV inversion concept has been successfully applied to real-time analysis and prediction systems, and to quantitatively evaluate the factors affecting the storm motions.

4.1. Background

Over the past 30 years, steady progress in the track forecasts of TCs has been made through the improvement of the numerical models, the data assimilation system, and the new data available to the forecast system (Wu, 2006). In addition to the large amount of satellite data, the special dropwindsonde data deployed from the surveillance aircraft have provided significant added value in improving the track forecasts.

In order to optimize the limited aircraft resources, targeted observations in the critical areas which have the maximum influence on numerical weather forecasts of TCs are of great importance. Therefore, targeted observing strategies for aircraft missions must be further developed. And it is a prerequisite for the device of observing strategy to identify the sensitive areas that have the greatest influence in improving the numerical forecast, or minimizing the track forecast error.

To make use of the available data or the potentially new data, it is important to evaluate the potential impact and to test the sensitivity of the simulation and prediction of TCs to different parameters. This understanding can be of great use in designing a cost-effective strategy for targeted observations of TCs (Morss et al., 2001; Majumdar et al. 2002a,b; Aberson, 2003; Wu et al., 2005).

In this section, three issues related to the author's works are addressed: (1) the impact of the DOTSTAR data; (2) results from a set of Observation System Simulation Experiments (OSSEs); (3) an innovative development of the new targeted observation strategy, the Adjoint-Derived Sensitivity Steering Vector (ADSSV).

4.2. Impact of dropwindsonde data on TC track forecasts from DOTSTAR

Since 2003, the research program of DOTSTAR (Wu et al., 2005, 2007b) has continuously conducted dropwindsonde observations of typhoons in the western North Pacific (Fig. 8). Three operational global and two regional models were used to evaluate the impact of the dropwindsonde on TC track forecasting (Wu et al., 2007b). Based on the results of 10 missions conducted in 2004 (Wu et al., 2007b), the use of the dropwindsonde data from DOTSTAR has improved the 72 h ensemble forecast of three global models, i.e. the Global Forecasting System (GFS) of National Centers for Environmental Prediction (NCEP), the Navy Operational Global Atmospheric Prediction System (NOGAPS) of the Fleet Numerical Meteorology and Oceanography Center (FNMOC), and the Japanese Meteorological Agency (JMA), Global Spectral Model (GSM), by 22% (Fig. 9).

Wu et al. (2007b) showed that the average improvement of the dropwindsonde data made by DOTSTAR to the 72 h typhoon track prediction in the Geophysical Fluid Dynamics Laboratory (GFDL) hurricane models is an insignificant 3%. It is very likely that the signal of the dropwindsonde data is swamped by the bogusing procedure used during the initialization of the GFDL hurricane model. Chou and Wu (2007) showed a better way of appropriately combining the dropwindsonde data with the bogused vortex in the mesoscale model in order to further boost the effectiveness of dropwindsonde data with the implanted storm vortex.

As the conventional observations usually have far less degrees of freedom than the models, the four-dimensional variational data assimilation

Figure 8. Best tracks (in typhoon symbols for every 24h) of the eight typhoons with ten DOTSTAR observation missions in 2004. The squares indicate the storm locations where the DOTSTAR missions were taken. The numbers on the squares represent the sequence of the missions. (From Wu et al., 2007b.)

Figure 9. 6-72 h mean track error reduction (in km) after the assimilation of the dropwindsonde data into each of the ten models. The storm's name is abbreviated to the first four letters, while Mini, Min2, and Min3 stand for the first, second, and third cases in Mindulle. (From Wu et al., 2007b.)

(4DVAR) has become one of the most advanced approaches to combining the observations with the model in such a way that the initial conditions are consistent with the model dynamics and physics (Guo et al., 2000). Based on

4DVAR, a bogus data assimilation method has been developed by Zou and Xiao (2000) to improve the initial conditions for TC simulation.

A set of OSSEs have been performed to identify the critical parameters and the improved procedures for the initialization and prediction of TCs. A control experiment is carried out to create the imaginary "nature" data for Typhoon Zane (1996), using the fifth-generation Pennsylvania State University -National Center for Atmospheric Research Mesoscale Model (MM5). Then the initial data from the control experiment are degraded to produce the new initial condition and simulation, which mimics typical global analysis that resolves the Zane circulation. By assimilating some variables from the initial data of the control experiment into the degraded initial condition based on 4DVAR, the insight into the key parameters for improving the initial condition and prediction of TCs is attained (Wu et al., 2006).

It is shown that the wind field is critical for maintaining a correct initial vortex structure of TCs. The model's memory of the pressure field is relatively short. Therefore, when only the surface pressure field is assimilated, due to the imbalance between the pressure and wind fields, the pressure field adjusts to the wind field and the minimal central sea-level pressure of the storm rises quickly.

It has been well demonstrated that taking the movement of the TC vortex into consideration during the data assimilation window can improve the track prediction, particularly in the early integration period. When the vortex movement tendency is taken into account during the bogus data assimilation period, it can partially correct the steering effect in the early prediction and the simulation period (Fig. 10). This concept provides a new and possible approach to the improvement of TC track prediction.

4.4. Targeted observations for TCs (Wu et al., 2007a)

(1) Adjoint-Derived Sensitivity Steering Vector (ADSSV)

By appropriately defining the response functions to represent the steering flow at the verifying

Figure 10. The 72 h JTWC best track (indicated with the typhoon symbol) and the simulated storm tracks from the experiments NO-DA, DA-FIX, and DA-MOVE for Typhoon Zeb (1998), shown for 12 h intervals from 0000 UTC, 13 October, to 0000 UTC, 16 October 1998. NO-DA: A standard MM5 simulation with an initial bogused vortex following Wu et al. (2002) without data assimilation. DA-FIX: An experiment assimilating the above bogused vortex (fixed in location) based on a 30-min-window 4DVAR data assimilation. DA-MOVE: An experiment in which the vortex is assimilated with the same initial data except that it moved in 3-h-window assimilation. (From Wu et al., 2006.)

Figure 10. The 72 h JTWC best track (indicated with the typhoon symbol) and the simulated storm tracks from the experiments NO-DA, DA-FIX, and DA-MOVE for Typhoon Zeb (1998), shown for 12 h intervals from 0000 UTC, 13 October, to 0000 UTC, 16 October 1998. NO-DA: A standard MM5 simulation with an initial bogused vortex following Wu et al. (2002) without data assimilation. DA-FIX: An experiment assimilating the above bogused vortex (fixed in location) based on a 30-min-window 4DVAR data assimilation. DA-MOVE: An experiment in which the vortex is assimilated with the same initial data except that it moved in 3-h-window assimilation. (From Wu et al., 2006.)

time, a simple innovative vector, Adjoint-Derived Sensitivity Steering Vector (ADSSV), has been designed to clearly demonstrate the sensitive locations and the critical direction of the typhoon steering flow at the observing time.

Because the goal is to identify the sensitive areas at the observing time that will affect the steering flow of the typhoon at the verifying time, the response function is defined as the deep-layer-mean wind within the verifying area. A 600-km-by-600-km-square area centered on the MM5-simulated storm location is used to calculate the background steering flow as defined by Chan and Gray (1982), and two response functions are defined: R\, the 850-300 hPa deep-layer area average (Wu et al., 2003) of the zonal component (u), along with R2, the average of the meridional component (v) of the wind vector, i.e.

r300hPa c iii

_ j850hpa JAu dxdydp c300 hPa rill Js50hPa j a dxdVdP

r300 hPa r iii

= JgsohPa Jav dxdydp

By averaging, the axisymmetric component of the strong cyclonic flow around the storm center is removed, and thus the vector of (Ri, R2) represents the background steering flow across the storm center at the verifying time. To interpret the physical meaning of the sensitivity, a unique new parameter, ADSSV, is designed to relate the sensitive areas at the observing time to the steering flow at the verifying time. The ADSSV with respect to the vorticity field (q) is fdR1 dR2

ADSSV =

\ dq 1 dq where the magnitude of the ADSSV at a given point indicates the extent of the sensitivity, and the direction of the ADSSV represents the change in the response of the steering flow due to a vorticity perturbation placed at that point. For example, an increase in the vorticity at the observing time would be associated with an increase in the eastward steering of the storm at the verifying time, given that the ADSSV at one particular grid point aims toward the east at the forecast time.

The ADSSV, based on the MM5 forecast (Fig. 11), extends about 300-600km from the north to the east of Typhoon Meari (2004). The directions of the ADSSVs indicate greater sensitivity in affecting the meridional component of the steering flow.

(2) Recent techniques for targeted observations of TCs

To optimize the aircraft surveillance observations using dropwindsondes, targeted observing strategies have been developed and examined. The primary consideration in devising such strategies is to identify the sensitive areas in which the assimilation of targeted observations is expected to have the greatest influence in improving the numerical forecast, or minimizing the forecast error. Since 2003, four objective methods have been tested for operational surveillance missions in the environment of Atlantic hurricanes conducted by National Oceanic and Atmospheric Administration (NOAA) (Aberson, 2003) and DOTSTAR (Wu et al., 2005). These products are derived from four distinct techniques: the ensemble deep-layer mean (DLM) wind variance (Aberson, 2003), the ensemble transform Kalman filter (ETKF; Majumdar et al., 2002), the total-energy singular vector (TESV) technique (Peng and Reynolds, 2006), and the Adjoint-Derived Sensitivity Steering Vector (ADSSV) (Wu et al., 2007a). These techniques have been applied in a limited capacity to identify locations for aircraft-borne dropwinsondes to be collected in the environment of the TCs. For the surveillance missions in Atlantic hurricanes conducted by NOAA Hurricane Research Division (HRD; Aberson, 2003) and DOTSTAR (Wu et al., 2005), besides the ADSSV method shown above, three other sensitivity techniques have been used to determine the observation strategies:

(i) Deep-layer 'mean (DLM) wind variance Based on the DLM (850-200-hPa-averaged) steering flows from the NCEP Global Ensemble Forecasting System (EFS; Aberson, 2003), areas with the largest (DLM) wind ensemble spread represent the sensitive regions at the observing time. The DLM wind ensemble spread is chosen because TCs are generally steered by the environmental DLM flow, and the dropwindsondes from the NOAA Gulfstream IV sample this flow.

Figure 11. The ADSSV with respect to the vorticity field at 700 hPa with 12 h (in green), 24 h (in red), and 36 h (in blue) as the verifying time, superposed with the geopotential height field (magnitude scaled by the color bar to the right; the unit is m) at 700 hPa and the deployed locations of the dropsondes in DOTSTAR (brown dots). The scale of the ADSSV is indicated as the arrow to the lower right (unit: m). The 36 h model-predicted track of Meari is indicated with the typhoon symbol in red for every 12 h. The three square boxes represent the verifying areas at three different verifying times. (From Wu et al., 2007a.)

Figure 11. The ADSSV with respect to the vorticity field at 700 hPa with 12 h (in green), 24 h (in red), and 36 h (in blue) as the verifying time, superposed with the geopotential height field (magnitude scaled by the color bar to the right; the unit is m) at 700 hPa and the deployed locations of the dropsondes in DOTSTAR (brown dots). The scale of the ADSSV is indicated as the arrow to the lower right (unit: m). The 36 h model-predicted track of Meari is indicated with the typhoon symbol in red for every 12 h. The three square boxes represent the verifying areas at three different verifying times. (From Wu et al., 2007a.)

of targeted observations based on the 40-member NCEP EFS (Majumdar et al., 2006). That is, the ETKF uses the differences among ensemble members to estimate regions for observational missions. It takes the approach of DLM wind variance further. While DLM wind variance indicates areas of forecast uncertainty at the observation time, it does not correlate initial condition uncertainty with the errors in the forecasts. The ETKF explicitly correlates errors at the observation time with errors of the forecasts and identifies ensemble variance that impacts the forecasts in the verifying area at the verifying time.

(iii) Singular vector (SV) technique The SV technique maximizes the growth of the total energy or kinetic energy norm (e.g. Palmer et al., 1998; Peng and Reynolds, 2006) using the adjoint and forward-tangent models of the NOGAPS; Rosmond, 1997; Gelaro et al., 2002), along with the ensemble prediction system

(EPS) of the JMA and the SV products from European Center for Medium-Range Weather Forecasts (ECMWF). Peng and Reynolds (2006) have demonstrated the capability of the SV technique in identifying the sensitive regions suitable for targeted observations of TCs.

The above techniques have been applied in a limited capacity to identify locations for aircraft-borne dropwinsondes to be collected in the environment of the TCs. To gain more physical insights into these targeted techniques, studies to compare and evaluate the techniques have been conducted by Majumdar et al. (2006), Etherton et al. (2006), and Reynolds et al. (2007).

4.5. Summary

DOTSTAR, a TC surveillance program using dropwindsondes, has been successfully launched since 2003. To capture the sensitive areas which may influence the TC track, a newly designed vector, ADSSV, has been proposed (Wu et al., 2007a). Aside from being used to conduct research on the impact of targeted observations, DOTSTAR's tropospheric soundings around the TC environment may also prove to be a unique dataset for the validation and calibration of remotely sensed data for TCs in the Northwest Pacific region.

Five models (four operational models and one research model) were used to evaluate the impact of dropwindsonde data on TC track forecasts during 2004. All models except the GFDL hurricane model show positive impacts from the dropwindsonde data on TC track forecasts. In the first 72 h, the mean track error reductions in the three operational global models, NCEP GFS, NOGAPS and JMA GSM, are 14%, 14%, and 19%, respectively, and the mean track error reduction of the ensemble of the three global models is 22%.

Along with the development of the ADSSV in DOTSTAR, an important issue on the targeted observations based on various techniques has been raised and should be further studied.

4.6. Further thoughts (Wu, 2006)

Experiments, such as the assimilation process of Numerical Weather Prediction (NWP) models conducted in recent years, have demonstrated their value in significantly reducing track forecast errors, suggesting that targeting observations are in need of more efforts. As reported at the 6th International Workshop on Tropical Cycones (Wu, 2006), some issues worth further exploration are:

(1) Research on targeted data should be extended to other observing systems and data (e.g. satellite-derived soundings). Application of new concepts in predictability and data assimilation should be tested.

(2) More studies of varying definitions, interpretations, and significance of sensitive regions (e.g. different methods, metrics) could be made.

(3) More work on metrics to assess the impact of targeting — or, more generally, on any changes in the observation network — should be done.

(4) Emphasis on the potential value of OSEs and OSSEs (e.g. Wu et al., 2006) in assessing potential observing system impacts prior to actual field programs is needed.

The author's perspective on the research works of TC motion has been presented in this article, and the major scientific contributions on TC motion issues from the author are summarized below:

(1) The baroclinic effect on TC motion (Wu and Emanuel 1993, 1994)

The dynamic properties of potential vorticity have been extensively utilized in observational work in meteorology. Potential vorticity concepts are first applied to the understanding of hurricane movement and hurricane structure, to a certain extent. Observations have shown that real TCs are strongly baroclinic, with broad anticyclones aloft. The interaction of the baroclinic hurricane vortex with background vertical shear may lead to storm drift, relative to the background mean flow, to the left (Northern Hemisphere) of the shear vector, and to a strong deformation of the outflow potential vor-ticity, resulting in jetlike outflow structure.

The potential vorticity diagnostics have been first designed to understand the controlling factors affecting the motion of typhoons. A newly proposed centroid-relative track, with the position weighting based on the steering flow induced by the PV anomaly associated with the other storm, has been plotted to highlight the binary interaction processes (Wu et al.,

2003). More detailed work has been conducted to evaluate and to quantify the physical factors that lead to the uncertainty of the typhoon movement, such as Sinlaku (2002) (Wu et al.,

2004). Further work is proposed to get into the physics of the statistical behavior of typhoon tracks in the whole of the western North Pacific region.

As described by Wu and Kuo (1999, BAMS), the improvement of the understanding of typhoon dynamics and typhoon forecasting in the Taiwan area hinges very much on the ability to incorporate the available data into high-resolution numerical models through advanced data assimilation techniques. The considerable efforts with data assimilation research are shown in Wu et al. (2006), which demonstrates the wind field to be the most important key variable affecting the initialization and simulation of typhoons. In addition, to obtain sufficient typhoon data and to improve TC track forecasts, a pioneering research and surveillance program for TCs in the western North Pacific, DOTSTAR, has been conducted (Wu et al., 2005). The flight routes enable observations in the most sensitive region around TCs, which is an area shown by several targeted observation methods, including the ADSSV, an innovative method developed by Wu et al. (2007a). It is believed that this adjoint sensitivity can be used to identify important areas and dynamical features affecting the TC track, and is helpful in constructing the strategy for adaptive observations. The ADSSV has been used among other methods for the targeted observations of typhoons in the western North Pacific (DOTSTAR) and hurricanes in the Atlantic (HRD's G-IV surverillance program).

Following the recommendation by Wu (2006), an intercomparison project has been initiated to evaluate the similarities and differences of all the different targeted techniques available. More analyses are ongoing to identify the similarities and differences of all these methods and to interpret their meaning dynamically. Results from this work would not only provide better insights into the physics of the targeted techniques, but also offer very useful information to assist future targeted observations. All this work is scheduled to be presented in a special selection on "Targeted Observation, Data Assimilation, and Tropical Cyclone Predictability" in the Monthly Weather Review of the American Meteorological Society.

Overall, DOTSTAR has had significant impact on the typhoon research and operation community in the international arena, and is also one of the key components of the newly developed project of T-PARC (THORPEX — Pacific Regional Campaign). Meanwhile, the Japanese team has also decided to conduct experiments (Typhoon Hunting 2008 — TH08) (T. Nakazawa, personal communication 2007) on targeted observations of TCs in 2008. It has been planned to fly two jets from both DOTSTAR and TH08 to target the same typhoon near the east of Taiwan and the south of Okinawa under T-PARC in 2008, so as to obtain the ideal and optimum dataset around the typhoon environment. With the potential international joint efforts of DOTSTAR and TH08 associated with T-PARC in 2008, the outlook for a further advance in the targeted observations and the predictability of the TC track is promising.

Acknowledgements

The author would like to thank all the collaborators for their contributions in the papers reviewed in this article. The helpful remarks of Yuqing Wang and another, anonymous reviewer are also appreciated. Special thanks also go to Prof. Po-Hsiung Lin and the COOK team on the DOTSTAR project, and the colleagues and students in my research group, "Typhoon Dynamics Research Center," at the Department of Atmospheric Sciences, National Taiwan University. The recent work is supported by the National Science Council of Taiwan through the grants NSC92-2119-M-002-009-AP1 and NSC93-2119-M-002-013-AP1, the Office of Naval Research grant N00014-05-1-0672, and MOTC-CWB-95-6M-03.

An important issue in the formation of concentric eyewalls in a typhoon is the development of a symmetric structure from asymmetric convection. As an idealization of the interaction of a tropical cyclone core with nearby weaker vorticity of various spatial scales, we consider nondivergent ba-rotropic model integrations to illustrate that concentric vorticity structures result from the interaction between a small and strong inner vortex (the tropical cyclone core) and neighboring weak vortices (the vorticity induced by the moist convection outside the central vortex of a tropical cyclone). In particular, the core vortex induces a differential rotation across the large and weak vortex, to strain out the latter into a vorticity band surrounding the former without a merging of the two. The straining out of a large, weak vortex into a concentric vorticity band can also result in the contraction of the outer tangential wind maximum. The dynamics highlight the essential role of the vorticity strength of the inner core vortex in maintaining itself, and in stretching, symmetrizing and stabilizing the outer vorticity field.

Our binary vortex experiments from the Rankine vortex suggest that the formation of a concentric vorticity structure requires: (1) a very strong core vortex with a vorticity at least six times stronger than the neighboring vortices, (2) a neighboring vorticity area that is larger than the core vortex, and (3) a separation distance between the neighboring vorticity field and the core vortex that is within three to four times the core vortex radius. On the other hand, when the companion vortex is four times larger than the core vortex in radius, a core vortex with a vorticity skirt produces concentric structures when the separation distance is five times greater than the smaller vortex. At this separation distance, the Rankine vortex produces elastic interaction. Thus, a skirted core vortex of sufficient strength can form a concentric vorticity structure at a larger radius than what is allowed by an unskirted core vortex. This may explain the wide range of radii for concentric eyewalls in observations.

1. Introduction

Aircraft observations of Hurricane Gilbert (1988) (e.g. Willoughby et al, 1982; Black and Willoughby, 1992, hereafter BW92) show that intense tropical cyclones often exhibit concentric eyewall patterns in their radar reflectivity. Approximately 12 hours after reaching its minimum sea level pressure of 888 hPa, the lowest recorded so far in the Atlantic basin (Willoughby et al., 1989), Hurricane Gilbert displayed concentric eyewalls. BW92 estimated the radius to be 8-20 km for the inner eyewall and 55-100 km for the outer eyewall. Between the two eyewalls, an echo-free gap (or moat) of about 35 km exists where the vorticity is low. In this pattern, deep convection within the inner, or primary, eyewall is surrounded by a nearly echo-free moat, which in turn is surrounded by a partial or complete ring of deep convection. Both convective regions typically contain well-defined local wind maxima and thus vorticity field. The primary wind maximum is associated with the inner core vortex, while the secondary wind maximum is usually associated with enhanced vorticity field embedded in the outer rainband (see e.g. the Hurricane Gilbert example given in Fig. 1 of Kossin et al, 2000).

Figure 1 shows the radar observations of Typhoon Lekima of 2001 (it has been adapted from Kuo et al, 2004; hereafter K04), and the passive microwave satellite data of Typhoon Imbudo (2003). The figure indicates that a huge area of convection outside the core vortex wraps around the inner eyewall to form the concentric eyewalls in a time scale of 12 hours for both cases. Figure 1 and that of BW92, along with many microwave images reported by Kuo and Schubert (2006; hereafter K06), suggest the formation of a concentric eyewall from the organization of asymmetric convection outside